Solution:

The distance from any point (x,y,z) to the point (0,0,0) is:

But if (x,y,z) lies on the surface , we have:

Solving for the critical points,

Substituting A) into B),

Therefore, (0,0) is a critical point.

Using the Second Derivative Test,

So, is a local minimum. Thus, the points on the surface closest to the origin are (0,0,1), (0,0,-1).

No Maple Code for this problem.